Rational Enriched Motivic Spaces

Enriched motivic $\mathcal{A}$-spaces are introduced and studied in this paper, where $\mathcal{A}$ is an additive category of correspondences. They are linear counterparts of motivic $\mathrm{\Gamma }$-spaces. It is shown that rational special enriched motivic $\widetilde{\mathrm{C}\mathrm{o}\mathrm{r}}$-spaces recover connective motivic bispectra with rational coefficients, where $\widetilde{\mathrm{C}\mathrm{o}\mathrm{r}}$ is the category of Milnor–Witt correspondences.